On some general properties of metrical operators generated by quadratic operator pencils

The article, which is a complementary one to the [3, 4], is devoted to the class of matrix operators generated by quadratic operator pencils. In terms of necessary and sufficient conditions on the elements of these matrices some theorems belonging to the known operator classes acting in usual Hilbert or indefinite Krein spaces have been formulated. Particularly, the necessary and sufficient conditions when the quadratic matrix operator is of Hilbert-Schmidt type or of nuclear type have been obtained.